A freind of mine that raises queen, this spring had some that only laid drones. What we figured was when it was time for the virgin flight the weather was bad and she didn't get breed. You could have a laying worker though. As far as shaking them out to other hives, depending on numbers etc, I would see about getting a queen myself.
Back this spring I had a hive swarm and there was no queen cell in the hive, I tried to find a queen, didn't, caught a swarm and was going to combine them. When checking that day before combining the two, I found a frame of worker brood. Put swarm in their own hive then. Hope it all works out for you.